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Category: Integration

x-tan-1-x-1-x-2-3-2-dx-

Question Number 89918 by jagoll last updated on 20/Apr/20 $$\int\:\frac{\mathrm{x}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}/\mathrm{2}} }\:\mathrm{dx}\: \\ $$ Commented by john santu last updated on 20/Apr/20 $$\left[\:{u}\:=\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:\Rightarrow{du}\:=\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}}…

Question-89736

Question Number 89736 by cindiaulia last updated on 19/Apr/20 Commented by jagoll last updated on 19/Apr/20 $$\mathrm{vol}\:=\:\pi\:\left[\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:\mathrm{dx}\:+\:\underset{\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:\left(\sqrt{\mathrm{x}}\right)^{\mathrm{2}} \:\mathrm{dx}\:\right] \\…

Question-89741

Question Number 89741 by cindiaulia last updated on 19/Apr/20 Commented by jagoll last updated on 19/Apr/20 $$\mathrm{area}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\mid\begin{vmatrix}{\mathrm{0}\:\:\:\:\:\mathrm{0}}\\{\mathrm{1}\:\:\:\:\:\mathrm{1}}\end{vmatrix}+\:\begin{vmatrix}{\mathrm{1}\:\:\:\:\:\:\mathrm{1}}\\{\frac{\mathrm{2}}{\mathrm{5}}\:\:\frac{\mathrm{8}}{\mathrm{5}}}\end{vmatrix}+\:\begin{vmatrix}{\frac{\mathrm{2}}{\mathrm{5}}\:\:\:\:\frac{\mathrm{8}}{\mathrm{5}}}\\{\mathrm{0}\:\:\:\:\:\:\:\mathrm{0}}\end{vmatrix}\mid \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\:\mid\:\mathrm{0}+\frac{\mathrm{6}}{\mathrm{5}}+\mathrm{0}\:\mid\:=\:\frac{\mathrm{3}}{\mathrm{5}} \\ $$ Terms of Service Privacy…

Question-89735

Question Number 89735 by cindiaulia last updated on 19/Apr/20 Commented by jagoll last updated on 19/Apr/20 $$\mathrm{red}\:\mathrm{parabola}\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\: \\ $$$$\mathrm{blue}\:\mathrm{parabola}\:\mathrm{y}\:=\:−\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4} \\ $$$$\mathrm{shaded}\:\mathrm{area}\::\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2x}\:=\:−\mathrm{x}^{\mathrm{2}} +\mathrm{4}…